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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 103488fx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103488.cq1 | 103488fx1 | \([0, -1, 0, -1633, 8065]\) | \(62500/33\) | \(254438080512\) | \([2]\) | \(92160\) | \(0.88008\) | \(\Gamma_0(N)\)-optimal |
103488.cq2 | 103488fx2 | \([0, -1, 0, 6207, 56673]\) | \(1714750/1089\) | \(-16792913313792\) | \([2]\) | \(184320\) | \(1.2267\) |
Rank
sage: E.rank()
The elliptic curves in class 103488fx have rank \(0\).
Complex multiplication
The elliptic curves in class 103488fx do not have complex multiplication.Modular form 103488.2.a.fx
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.